The surface diffusion flow for immersed hypersurfaces

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  • University of Basel
  • Vanderbilt University
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Details

Original languageEnglish
Pages (from-to)1419-1433
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume29
Issue number6
Publication statusPublished - Nov 1998
Externally publishedYes

Abstract

We show existence and uniqueness of classical solutions for the motion of immersed hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a sphere, we prove that the solution exists globally and converges exponentially fast to a sphere. Furthermore, we provide numerical simulations showing the creation of singularities for immersed curves.

Keywords

    Center manifolds, Free boundary problem, Immersed hypersurfaces, Maximal regularity, Mean curvature, Numerical simulations, Surface diffusion

ASJC Scopus subject areas

Cite this

The surface diffusion flow for immersed hypersurfaces. / Escher, Joachim; Mayer, Uwe F.; Simonett, Gieri.
In: SIAM Journal on Mathematical Analysis, Vol. 29, No. 6, 11.1998, p. 1419-1433.

Research output: Contribution to journalArticleResearchpeer review

Escher J, Mayer UF, Simonett G. The surface diffusion flow for immersed hypersurfaces. SIAM Journal on Mathematical Analysis. 1998 Nov;29(6):1419-1433. doi: 10.1137/S0036141097320675
Escher, Joachim ; Mayer, Uwe F. ; Simonett, Gieri. / The surface diffusion flow for immersed hypersurfaces. In: SIAM Journal on Mathematical Analysis. 1998 ; Vol. 29, No. 6. pp. 1419-1433.
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KW - Maximal regularity

KW - Mean curvature

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